Question

In the diagram below of triangle A, B, CABC, DD is the midpoint of start overline, A, C, end overline
AC
and EE is the midpoint of start overline, B, C, end overline
BC
. If mangle, C, A, B, equals, 58, minus, 2, x∠CAB=58−2x, and mangle, C, D, E, equals, 2, x, plus, 54∠CDE=2x+54, what is the measure of angle, C, A, B∠CAB?

Answer 1

DE is the midsegment joining midpoints of AC and BC, so DE ∥ AB. Thus ∠CDE is corresponding to ∠CAB, so 58 − 2x = 2x + 54.
Solve: 58 − 54 = 4x ⇒ 4 = 4x ⇒ x = 1.
Therefore ∠CAB = 58 − 2(1) = 56°.